We have all probably wondered how great minds achieved what they achieved, right? And the more astonishing their achievements are, the more we call them geniuses, perhaps aliens coming from a different planet, definitely not someone like us. But is that true?

So let me start with an example. You all know the story of Newton's apple, right? OK. Is that true? Probably not. Still, it's difficult to think that no apple at all was there. I mean some stepping stone, some specific conditions that made universal gravitation not impossible to conceive. And definitely this was not impossible, at least for Newton. It was possible, and for some reason, it was also there, available at some point, easy to pick as an apple. Here is the apple.

And what about Einstein? Was relativity theory another big leap in the history of ideas no one else could even conceive? Or rather, was it again something adjacent and possible, to Einstein of course, and he got there by small steps and his very peculiar scientific path? Of course we cannot conceive this path, but this doesn't mean that the path was not there. So all of this seems very evocative, but I would say hardly concrete if we really want to grasp the origin of great ideas and more generally the way in which the new enters our lives. As a physicist, as a scientist, I have learned that posing the right questions is half of the solution. But I think now we start having a great conceptual framework to conceive and address the right questions. So let me drive you to the edge of what is known, or at least, what I know, and let me show you that what is known could be a powerful and fascinating starting point to grasp the deep meaning of words like novelty, innovation, creativity perhaps.

So we are discussing the "new," and of course, the science behind it. The new can enter our lives in many different ways, can be very personal, like I meet a new person, I read a new book, or I listen to a new song. Or it could be global, I mean, something we call innovation. It could be a new theory, a new technology, but it could also be a new book if you're the writer, or it could be a new song if you're the composer. In all of these global cases, the new is for everyone, but experiencing the new can be also frightening, so the new can also frighten us. But still, experiencing the new means exploring a very peculiar space, the space of what could be, the space of the possible, the space of possibilities. It's a very weird space, so I'll try to get you through this space. So it could be a physical space. So in this case, for instance, novelty could be climbing Machu Picchu for the first time, as I did in 2016. It could be a conceptual space, so acquiring new information, making sense of it, in a word, learning. It could be a biological space. I mean, think about the never-ending fight of viruses and bacteria with our immune system.

And now comes the bad news. We are very, very bad at grasping this space. Think of it. Let's make an experiment. Try to think about all the possible things you could do in the next, say, 24 hours. Here the key word is "all." Of course you can conceive a few options, like having a drink, writing a letter, also sleeping during this boring talk, if you can. But not all of them. So think about an alien invasion, now, here, in Milan, or me—I stopped thinking for 15 minutes.

So it's very difficult to conceive this space, but actually we have an excuse. So it's not so easy to conceive this space because we are trying to conceive the occurrence of something brand new, so something that never occurred before, so we don't have clues. A typical solution could be looking at the future with the eyes of the past, so relying on all the time series of past events and hoping that this is enough to predict the future. But we know this is not working. For instance, this was the first attempt for weather forecasts, and it failed. And it failed because of the great complexity of the underlying phenomenon. So now we know that predictions had to be based on modeling, which means creating a synthetic model of the system, simulating this model and then projecting the system into the future through this model. And now we can do this in a lot of cases with the help of a lot of data.

Looking at the future with the eye of the past could be misleading also for machines. Think about it. Now picture yourself for a second in the middle of the Australian Outback. You stand there under the sun. So you see something weird happening. The car suddenly stops very, very far from a kangaroo crossing the street. You look closer and you realize that the car has no driver. It is not restarting, even after the kangaroo is not there anymore. So for some reasons, the algorithms driving the car cannot make sense of this strange beast jumping here and there on the street. So it just stops. Now, I should tell you, this is a true story. It happened a few months ago to Volvo's self-driving cars in the middle of the Australian Outback.

It is a general problem, and I guess this will affect more and more in the near future artificial intelligence and machine learning. It's also a very old problem, I would say 17th century, but I guess now we have new tools and new clues to start solving it.

So let me take a step back, five years back. Italy. Rome. Winter. So the winter of 2012 was very special in Rome. Rome witnessed one of the greatest snowfalls of its history. That winter was special also for me and my colleagues, because we had an insight about the possible mathematical scheme—again, possible, possible mathematical scheme, to conceive the occurrence of the new. I remember that day because it was snowing, so due to the snowfall, we were blocked, stuck in my department, and we couldn't go home, so we got another coffee, we relaxed and we kept discussing. But at some point—maybe not that date, precisely—at some point we made the connection between the problem of the new and a beautiful concept proposed years before by Stuart Kauffman, the adjacent possible. So the adjacent possible consists of all those things. It could be ideas, it could be molecules, it could be technological products that are one step away from what actually exists, and you can achieve them through incremental modifications and recombinations of the existing material.

So for instance, if I speak about the space of my friends, my adjacent possible would be the set of all friends of my friends not already my friends. I hope that's clear. But now if I meet a new person, say Briar, all her friends would immediately enter my adjacent possible, pushing its boundaries further. So if you really want to look from the mathematical point of view—I'm sure you want—you can actually look at this picture. So suppose now this is your universe. I know I'm asking a lot. I mean, this is your universe. Now you are the red spot. And the green spot is the adjacent possible for you, so something you've never touched before. So you do your normal life. You move. You move in the space. You have a drink. You meet friends. You read a book. At some point, you end up on the green spot, so you meet Briar for the first time. And what happens? So what happens is there is a new part, a brand new part of the space, becoming possible for you in this very moment, even without any possibility for you to foresee this before touching that point. And behind this there will be a huge set of points that could become possible at some later stages. So you see the space of the possible is very peculiar, because it's not predefined. It's not something we can predefine. It's something that gets continuously shaped and reshaped by our actions and our choices.

So we were so fascinated by these connections we made—scientists are like this. And based on this, we conceived our mathematical formulation for the adjacent possible, 20 years after the original Kauffman proposals. In our theory—this is a key point—I mean, it's crucially based on a complex interplay between the way in which this space of possibilities expands and gets restructured, and the way in which we explore it.

After the epiphany of 2012, we got back to work, real work, because we had to work out this theory, and we came up with a certain number of predictions to be tested in real life. Of course, we need a testable framework to study innovation. So let me drive you across a few predictions we made. The first one concerns the pace of innovation, so the rate at which you observe novelties in very different systems. So our theory predicts that the rate of innovation should follow a universal curve, like this one. This is the rate of innovation versus time in very different conditions. And somehow, we predict that the rate of innovation should decrease steadily over time. So somehow, innovation is predicted to become more difficult as your progress over time.

It's neat. It's interesting. It's beautiful. We were happy. But the question is, is that true? Of course we should check with reality.

So we went back to reality and we collected a lot of data, terabytes of data, tracking innovation in Wikipedia, Twitter, the way in which we write free software, even the way we listen to music. I cannot tell you, we were so amazed and pleased and thrilled to discover that the same predictions we made in the theory were actually satisfied in real systems, many different real systems. We were so excited. Of course, apparently, we were on the right track, but of course, we couldn't stop, so we didn't stop. So we kept going on, and at some point we made another discovery that we dubbed "correlated novelties." It's very simple. So I guess we all experience this. So you listen to "Suzanne" by Leonard Cohen, and this experience triggers your passion for Cohen so that you start frantically listening to his whole production. And then you realize that Fabrizio De Andre here recorded an Italian version of "Suzanne," and so on and so forth. So somehow for some reason, the very notion of adjacent possible is already encoding the common belief that one thing leads to another in many different systems. But the reason why we were thrilled is because actually we could give, for the first time, a scientific substance to this intuition and start making predictions about the way in which we experience the new. So novelties are correlated. They are not occurring randomly. And this is good news, because it implies that impossible missions might not be so impossible after all, if we are guided by our intuition, somehow leading us to trigger a positive chain reaction. But there is a third consequence of the existence of the adjacent possible that we named "waves of novelties." So just to make this simple, so in music, without waves of novelties, we would still be listening all the time to Mozart or Beethoven, which is great, but we don't do this all the time. We also listen to the Pet Shop Boys or Justin Bieber—well, some of us do.

So we could see very clearly all of these patterns in the huge amounts of data we collected and analyzed. For instance, we discovered that popular hits in music are continuously born, you know that, and then they disappear, still leaving room for evergreens. So somehow waves of novelties ebb and flow while the tides always hold the classics. There is this coexistence between evergreens and new hits. Not only our theory predicts these waves of novelties. This would be trivial. But it also explains why they are there, and they are there for a specific reason, because we as humans display different strategies in the space of the possible. So some of us tend to retrace already known paths. So we say they exploit. Some of us always launch into new adventures. We say they explore. And what we discovered is all the systems we investigated are right at the edge between these two strategies, something like 80 percent exploiting, 20 percent exploring, something like blade runners of innovation. So it seems that the wise balance, you could also say a conservative balance, between past and future, between exploitation and exploration, is already in place and perhaps needed in our system. But again the good news is now we have scientific tools to investigate this equilibrium, perhaps pushing it further in the near future.

So as you can imagine, I was really fascinated by all this. Our mathematical scheme is already providing cues and hints to investigate the space of possibilities and the way in which all of us create it and explore it. But there is more. This, I guess, is a starting point of something that has the potential to become a wonderful journey for a scientific investigation of the new, but also I would say a personal investigation of the new. And I guess this can have a lot of consequences and a huge impact in key activities like learning, education, research, business. So for instance, if you think about artificial intelligence, I am sure—I mean, artificial intelligence, we need to rely in the near future more and more on the structure of the adjacent possible, to restructure it, to change it, but also to cope with the unknowns of the future. In parallel, we have a lot of tools, new tools now, to investigate how creativity works and what triggers innovation. And the aim of all this is to raise a generation of people able to come up with new ideas to face the challenges in front of us. We all know. I think it's a long way to go, but the questions, and the tools, are now there, adjacent and possible. Thank you.